Axiomatization of Shapley Values of Fagle and Kern Type on Set Systems

2008 ◽  
Vol 12 (5) ◽  
pp. 409-415 ◽  
Author(s):  
Aoi Honda ◽  
◽  
Yoshiaki Okazaki
Keyword(s):  
Cooperative Game ◽  
Shapley Value ◽  
Potential Application ◽  
Set Systems ◽  
Shapley Values

We propose axiomatizing a generalized Shapley value of games for potential application to games on set systems satisfying the condition of normality. This encompasses both the original Shapley value and Faigle and Kern's Shapley value, which is generalized for a cooperative game defined on a subcoalition.

Shapley Ranking of Wines

2012 ◽  
Vol 7 (2) ◽  
pp. 169-180 ◽  
Author(s):  
Victor Ginsburgh ◽  
Israël Zang
Keyword(s):  
Game Theory ◽  
Unique Solution ◽  
Cooperative Game ◽  
Shapley Value ◽  
Rank Order ◽  
Jel Classification ◽  
Ranking Method ◽  
The Shapley Value ◽  
Shapley Values

AbstractWe suggest a new game-theory-based ranking method for wines, in which the Shapley Value of each wine is computed, and wines are ranked according to their Shapley Values. Judges should find it simpler to use, since they are not required to rank order or grade all the wines, but merely to choose the group of those that they find meritorious. Our ranking method is based on the set of reasonable axioms that determine the Shapley Value as the unique solution of an underlying cooperative game. Unlike in the general case, where computing the Shapley Value could be complex, here the Shapley Value and hence the final ranking, are straightforward to compute. (JEL Classification: C71, D71, D78)

A novel q-rung orthopair fuzzy TODIM approach for multi-criteria group decision making based on Shapley value and relative entropy

2021 ◽  
Vol 40 (1) ◽  
pp. 235-250
Author(s):  
Liuxin Chen ◽  
Nanfang Luo ◽  
Xiaoling Gou
Keyword(s):  
Decision Making ◽  
Relative Entropy ◽  
Group Decision Making ◽  
Shapley Value ◽  
Group Decision ◽  
Similarity Measures ◽  
Entropy Measure ◽  
Shapley Values ◽  
Interactive Relationship ◽  
The Difference

In the real multi-criteria group decision making (MCGDM) problems, there will be an interactive relationship among different decision makers (DMs). To identify the overall influence, we define the Shapley value as the DM’s weight. Entropy is a measure which makes it better than similarity measures to recognize a group decision making problem. Since we propose a relative entropy to measure the difference between two systems, which improves the accuracy of the distance measure.In this paper, a MCGDM approach named as TODIM is presented under q-rung orthopair fuzzy information.The proposed TODIM approach is developed for correlative MCGDM problems, in which the weights of the DMs are calculated in terms of Shapley values and the dominance matrices are evaluated based on relative entropy measure with q-rung orthopair fuzzy information.Furthermore, the efficacy of the proposed Gq-ROFWA operator and the novel TODIM is demonstrated through a selection problem of modern enterprises risk investment. A comparative analysis with existing methods is presented to validate the efficiency of the approach.

Query Games in Databases

2021 ◽  
Vol 50 (1) ◽  
pp. 78-85
Author(s):  
Ester Livshits ◽  
Leopoldo Bertossi ◽  
Benny Kimelfeld ◽  
Moshe Sebag
Keyword(s):  
Game Theory ◽  
Cooperative Game ◽  
Shapley Value ◽  
Cooperative Game Theory ◽  
The Shapley Value ◽  
Computational Aspects ◽  
Aggregate Query ◽  
Boolean Query

Database tuples can be seen as players in the game of jointly realizing the answer to a query. Some tuples may contribute more than others to the outcome, which can be a binary value in the case of a Boolean query, a number for a numerical aggregate query, and so on. To quantify the contributions of tuples, we use the Shapley value that was introduced in cooperative game theory and has found applications in a plethora of domains. Specifically, the Shapley value of an individual tuple quantifies its contribution to the query. We investigate the applicability of the Shapley value in this setting, as well as the computational aspects of its calculation in terms of complexity, algorithms, and approximation.

A New Collaborative Filtering Approach Based on Game Theory for Recommendation Systems

2021 ◽  
Author(s):  
Selma Benkessirat ◽  
Narhimene Boustia ◽  
Rezoug Nachida
Keyword(s):  
Game Theory ◽  
Collaborative Filtering ◽  
Cooperative Game ◽  
Shapley Value ◽  
Cooperative Game Theory ◽  
Recommendation Systems ◽  
Internet Users ◽  
User Communities ◽  
The One

Recommendation systems can help internet users to find interesting things that match more with their profile. With the development of the digital age, recommendation systems have become indispensable in our lives. On the one hand, most of recommendation systems of the actual generation are based on Collaborative Filtering (CF) and their effectiveness is proved in several real applications. The main objective of this paper is to improve the recommendations provided by collaborative filtering using clustering. Nevertheless, taking into account the intrinsic relationship between users can enhance the recommendations performances. On the other hand, cooperative game theory techniques such as Shapley Value, take into consideration the intrinsic relationship among users when creating communities. With that in mind, we have used SV for the creation of user communities. Indeed, our proposed algorithm preforms into two steps, the first one consists to generate communities user based on Shapley Value, all taking into account the intrinsic properties between users. It applies in the second step a classical collaborative filtering process on each community to provide the Top-N recommendation. Experimental results show that the proposed approach significantly enhances the recommendation compared to the classical collaborative filtering and k-means based collaborative filtering. The cooperative game theory contributes to the improvement of the clustering based CF process because the quality of the users communities obtained is better.

Importance measures for degrading components based on cooperative game theory

2019 ◽  
Vol 37 (2) ◽  
pp. 189-206
Author(s):  
Yingsai Cao ◽  
Sifeng Liu ◽  
Zhigeng Fang
Keyword(s):  
Cooperative Game ◽  
Shapley Value ◽  
System Reliability ◽  
Design Methodology ◽  
System Structure ◽  
Importance Measure ◽  
Engineering Systems ◽  
Content Type ◽  
Timely Feedback ◽  
Degradation Models

Purpose The purpose of this paper is to propose new importance measures for degrading components based on Shapley value, which can provide answers about how important players are to the whole cooperative game and what payoff each player can reasonably expect. Design/methodology/approach The proposed importance measure characterizes how a specific degrading component contributes to the degradation of system reliability by using Shapley value. Degradation models are also introduced to assess the reliability of degrading components. The reliability of system consisting independent degrading components is obtained by using structure functions, while reliability of system comprising correlated degrading components is evaluated with a multivariate distribution. Findings The ranking of degrading components according to the newly developed importance measure depends on the degradation parameters of components, system structure and parameters characterizing the association of components. Originality/value Considering the fact that reliability degradation of engineering systems and equipment are often attributed to the degradation of a particular or set of components that are characterized by degrading features. This paper proposes new importance measures for degrading components based on Shapley value to reflect the responsibility of each degrading component for the deterioration of system reliability. The results are also able to give timely feedback of the expected contribution of each degrading component to system reliability degradation.

scholarly journals The Shapley Values on Fuzzy Coalition Games with Concave Integral Form

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Jinhui Pang ◽  
Xiang Chen ◽  
Shujin Li
Keyword(s):  
Cooperative Game ◽  
Integral Form ◽  
Simple Calculation ◽  
Calculation Formula ◽  
Concave Integral ◽  
Shapley Values ◽  
Linear Aggregation ◽  
Fuzzy Game ◽  
Expected Values

A generalized form of a cooperative game with fuzzy coalition variables is proposed. The character function of the new game is described by the Concave integral, which allows players to assign their preferred expected values only to some coalitions. It is shown that the new game will degenerate into the Tsurumi fuzzy game when it is convex. The Shapley values of the proposed game have been investigated in detail and their simple calculation formula is given by a linear aggregation of the Shapley values on subdecompositions crisp coalitions.

scholarly journals Redistribution of tax resources: a cooperative game theory approach

SERIEs ◽  
2021 ◽  
Author(s):  
Emilio Calvo
Keyword(s):  
Cooperative Game ◽  
Shapley Value ◽  
Financial System ◽  
Budget Allocation ◽  
Theory Approach ◽  
Moderate Degree ◽  
Allocation Rules ◽  
Economic Entity ◽  
Balanced Allocation ◽  
The Stability

AbstractWe consider the problem of how to distribute public expenditure among the different regions of an economic entity after all taxes have been collected. Typical examples are: the regions that make up a country, the states of a federal country, or the countries of a confederation of countries. We model the problem as a cooperative game in coalitional form, called the tax game. This game estimates the fiscal resources collected in each region, or coalition of regions, by differentiating between what comes from economic activity within each region and what comes from trade with the other regions. This methodology provides a measure of the disagreement within a region, or coalitions of regions, with respect to the budget received. Similarly, the stability of a budget allocation can be inferred by its situation within the core of the corresponding tax game. We consider the Spanish case as an example and show that the current regional financial system has a moderate degree of instability. We introduce two budget allocation rules, both borrowed from the cooperative games literature: the balanced allocation, which coincides with the nucleolus and with the Shapley value of the tax game, and the weighted balanced allocation, which coincides with the weighted Shapley value. We compare both budget allocation rules with the current Spanish financial system.

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